The primary question faced by the operator of a taxi network is how to distribute cabs to maximize revenue (or minimize cost). This is a type of a inventory control problem with stochastic components that may increase or decrease inventory at a given location. The cab network operator experiences stochastic demand for trips which distribute the cabs across a city according to the patterns of daily routine and is then faced with the question of how to best direct cabs throughout the day to optimize revenue. Or put simply, “where should I park my cab between trips?” and the closely related question, “how many cabs do I need at a minimum?” The problem also informs the regulator, “what is the effect of changing regulation on the efficiency of meeting ridership demand?”
New York City recently released information on all taxi trips throughout the city between 2009 and mid 2015. This information allows the modeling of the demand for taxi rides and their redistributive effect on cab stock in each neighborhood. With the judicious use of assumptions regarding the nature of cab revenue and costs as well as the application of other simplifying strategies it is possible to construct the optimization problem facing a cab system operator.
First, a look at the effect of demand on taxi distribution. The following are plots of net taxi trips into given spatial regions (tract or burough) over every 15 minute interval during a representative Monday from the entire dataset (straight averaging, no conditioning on holidays). The tract level modeling may appear execessive, but due to the depth of the data the vast majority of spatial heterogeneity here is signal, not noise. Note that to show variation the scale has been clipped in both images, so pay careful attention to the fully saturated regions.